Topology sheds new light on the emergence of unidirectional edge waves in a variety of physical systems, from condensed matter to artificial lattices. Waves observed in geophysical flows are also robust to perturbations, which suggests a role for topology. We show a topological origin for two well-known equatorially trapped waves, the Kelvin and Yanai modes, owing to the breaking of time-reversal symmetry by Earth’s rotation. The nontrivial structure of the bulk Poincaré wave modes encoded through the first Chern number of value 2 guarantees the existence of these waves. This invariant demonstrates that ocean and atmospheric waves share fundamental properties with topological insulators and that topology plays an unexpected role in Earth’s climate system.